Abstract: In this talk, we establish the invariance of weak observability for the observed backward stochastic differential equations (BSDEs) with constant coefficients, relative to the filtered probability space. This signifies that the weak observability of these observed BSDEs with constant coefficients remains unaffected by the selection of the filtered probability space. As an illustrative application, we demonstrate that for stochastic control systems with constant coefficients, weak observability, approximate null controllability with cost, and stabilizability are equivalent across some or any filtered probability spaces.

This is a joint work with Bao-Zhu Guo, Meixuan Zhang.